Question

extra credit: $x^2 cdot x^3$ can be written as the product of __ factors of and the product of factors of . in all, there are factors of which can be written as the exponential expression of __.

Explanation:

Step1: Identify first term's factors

$x^2$ is 2 factors of $x$: $x \cdot x$

Step2: Identify second term's factors

$x^3$ is 3 factors of $x$: $x \cdot x \cdot x$

Step3: Count total factors

Add the number of factors: $2 + 3 = 5$

Step4: Write exponential form

Combine using exponent rule: $x^2 \cdot x^3 = x^{2+3} = x^5$

Answer:

$x^2 \cdot x^3$ can be written as the product of $\boldsymbol{2}$ factors of $\boldsymbol{x}$, and the product of $\boldsymbol{3}$ factors of $\boldsymbol{x}$. In all, there are $\boldsymbol{5}$ factors of $\boldsymbol{x}$ which can be written as the exponential expression of $\boldsymbol{x^5}$.